On sets minimizing their weighted length in uniformly convex separable Banach spaces

Thierry de Pauw (1) , Antoine Lemenant (2) , Vincent Millot (2)

1 Projet Géométrie et Dynamique
2 LJLL - Laboratoire Jacques-Louis Lions

We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show C^1 regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.

Mots clés: almost minimal set; Steiner problem; partial regularity

Domaines: Analyse classique [math.CA]; Géométrie métrique [math.MG]

Thierry de Pauw, Antoine Lemenant, Vincent Millot. On sets minimizing their weighted length in uniformly convex separable Banach spaces. Advances in Mathematics, 2017, 305. ⟨hal-00877498⟩